A note on costs minimization with stochastic target constraints

Yan Dolinsky; Benjamin Gottesman; Ori Gurel-Gurevich

doi:10.1214/20-ECP295

A note on costs minimization with stochastic target constraints

Yan Dolinsky, Benjamin Gottesman, Ori Gurel-Gurevich

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

We study the minimization of the expected costs under stochastic constraint at the terminal time. The first and the main result says that for a power type of costs, the value function is the minimal positive solution of a second order semi-linear ordinary differential equation (ODE). Moreover, we establish the optimal control. In the second example we show that the case of exponential costs leads to a trivial optimal control.

Original language	American English
Article number	11
Journal	Electronic Communications in Probability
Volume	25
DOIs	https://doi.org/10.1214/20-ECP295
State	Published - 2020

Bibliographical note

Funding Information:
Acknowledgments. We would like to thank the anonymous reviewers for their suggestions and comments which improved the paper. We also would like to thank Peter Bank, Asaf Cohen and Ross Pinsky for valuable discussions. This research was partially supported by the ISF grant no 160/17 and the ISF grant no 1707/16.

Publisher Copyright:
© 2020, Institute of Mathematical Statistics. All rights reserved.

Keywords

Backward stochastic differential equations
Optimal stochastic control

Access to Document

10.1214/20-ECP295

Cite this

@article{2ce04926f28b498fb071879f88e49154,

title = "A note on costs minimization with stochastic target constraints",

abstract = "We study the minimization of the expected costs under stochastic constraint at the terminal time. The first and the main result says that for a power type of costs, the value function is the minimal positive solution of a second order semi-linear ordinary differential equation (ODE). Moreover, we establish the optimal control. In the second example we show that the case of exponential costs leads to a trivial optimal control.",

keywords = "Backward stochastic differential equations, Optimal stochastic control",

author = "Yan Dolinsky and Benjamin Gottesman and Ori Gurel-Gurevich",

note = "Funding Information: Acknowledgments. We would like to thank the anonymous reviewers for their suggestions and comments which improved the paper. We also would like to thank Peter Bank, Asaf Cohen and Ross Pinsky for valuable discussions. This research was partially supported by the ISF grant no 160/17 and the ISF grant no 1707/16. Publisher Copyright: {\textcopyright} 2020, Institute of Mathematical Statistics. All rights reserved.",

year = "2020",

doi = "10.1214/20-ECP295",

language = "American English",

volume = "25",

journal = "Electronic Communications in Probability",

issn = "1083-589X",

publisher = "Institute of Mathematical Statistics",

}

TY - JOUR

T1 - A note on costs minimization with stochastic target constraints

AU - Dolinsky, Yan

AU - Gottesman, Benjamin

AU - Gurel-Gurevich, Ori

N1 - Funding Information: Acknowledgments. We would like to thank the anonymous reviewers for their suggestions and comments which improved the paper. We also would like to thank Peter Bank, Asaf Cohen and Ross Pinsky for valuable discussions. This research was partially supported by the ISF grant no 160/17 and the ISF grant no 1707/16. Publisher Copyright: © 2020, Institute of Mathematical Statistics. All rights reserved.

PY - 2020

Y1 - 2020

N2 - We study the minimization of the expected costs under stochastic constraint at the terminal time. The first and the main result says that for a power type of costs, the value function is the minimal positive solution of a second order semi-linear ordinary differential equation (ODE). Moreover, we establish the optimal control. In the second example we show that the case of exponential costs leads to a trivial optimal control.

AB - We study the minimization of the expected costs under stochastic constraint at the terminal time. The first and the main result says that for a power type of costs, the value function is the minimal positive solution of a second order semi-linear ordinary differential equation (ODE). Moreover, we establish the optimal control. In the second example we show that the case of exponential costs leads to a trivial optimal control.

KW - Backward stochastic differential equations

KW - Optimal stochastic control

UR - http://www.scopus.com/inward/record.url?scp=85079056858&partnerID=8YFLogxK

U2 - 10.1214/20-ECP295

DO - 10.1214/20-ECP295

M3 - Article

AN - SCOPUS:85079056858

SN - 1083-589X

VL - 25

JO - Electronic Communications in Probability

JF - Electronic Communications in Probability

M1 - 11

ER -

A note on costs minimization with stochastic target constraints

Abstract

Bibliographical note

Keywords

Access to Document

Other files and links

Fingerprint

Cite this